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IP Assignment: Chi-Square Test Essay

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Postulating Hypotheses

Within the proposed scenario, there are two strategic options for the company’s further development, which include maintaining its position in the current market or expanding into other markets. It is on the basis of these options that two research hypotheses should be formulated. Thus, the null hypothesis assumes the option of preservation in the current market. The alternative hypothesis, on the contrary, reports that entering the following markets will be more effective for the company.

Description of the Selected Method

A non-parametric Chi-Square test based on qualitative data will be used to analyze the data. This nature of the variables is due to their non-numerical measurement, which means that the data should be categorical values: for example, the preferences of customers from different market segments for specific sporting goods of the store. Such preferences may consist of the names of specific items or categories, whether they are outdoor products, camping products, or sports balls. For this reason, the data are not numbers but categories, the distance between which cannot be measured.

Nevertheless, for statistical analysis, there is a need to work with qualitative data as well. The results of such an analysis allow us to describe the significance of differences between categories, such as how much more consumers from one market segment buy sports balls than from another. For this reason, the Chi-Square test is excellent for comparing differences between categorical data, which satisfies the conditions of the scenario. It should be noted, however, that this test is non-parametric. The non-parametric nature of the method is due to the lack of the need to evaluate for assumptions about the normality of the distribution; that is, the data for analysis do not necessarily have to be distributed bell-shaped (Manoukian, 2022). It is important to note, however, that the absence of such an assumption test does not mean that the results cannot be extrapolated to the population.

In general, this test can be based on manual or automatic calculations, depending on the resources available. In either case, the Chi-Square test deals with frequency distribution tables (Bozeman Science, 2011). Such tables are constructed from categorical columns and rows with values at the intersection. An example of such a table would be the number of times consumers from different segments chose a given sporting product, which is actually a numerical comparison of preferences. The frequencies used in the table are called observed frequencies; that is, they reflect the real agenda for these categories based on the sample. However, the Chi-Square test also requires expected frequencies, which can be calculated using the formula (Row Total * Column Total)/N. Accordingly, there will be a unique expected frequency for each of the cells in the table. The Chi-Square test criterion is calculated using the formula χ2 = ∑(Oi – Ei)2/Ei , resulting in a specific number. The significance test also requires the specification of the number of degrees of freedom, which is calculated as the product of the number of rows (minus one) by the number of columns (minus one) for the table.

When the value of the test statistic and the number of degrees of freedom are found, it is possible to calculate a p-value for these data on the basis of standard tables. Comparing this calculated value to a critical level of significance (for example,.05) allows you to determine the statistical significance of the results and accept or reject the null hypothesis. In particular, if the calculated p-value is less than.05, then the null hypothesis must be rejected because there is substantial evidence against it. In other words, these results will show that the company needs to enter new markets because customer preferences from there appear to be significant. This will determine the further strategic development of the company based on reliable conclusions.

References

Bozeman Science. (2011). [Video]. YouTube. Web.

Manoukian, E. B. (2022). Mathematical nonparametric statistics. Taylor & Francis.

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